ON THE EXISTENCE OF CERTAIN MODULES OF FINITE GORENSTEIN HOMOLOGICAL DIMENSIONS

摘要

Let (R,m) be a commutative Noetherian local ring. It is known that R is Cohen- Macaulay if there exists either a nonzero finitely generated R-module of finite injective dimension or a nonzero Cohen-Macaulay R-module of finite projective dimension. In this article, we investigate the Gorenstein analogues of these facts.